Robust spectrum management with incomplete information over fading channels

Abstract

This paper studies a wireless interference game in fading channels with partial channel state information. Using a Bayesian game formulation, we consider two selfish wireless communication systems (players) who share the same frequency band, where each player only knows its own channel gains up to some estimation error. Based on that knowledge, the players take decisions on whether to spread their transmit power over the whole spectrum, or to employ frequency division duplexing. In the case of fixed channels with perfect channel estimation, this game is known to have a spectrally efficient equilibrium point, in comparison to the equilibrium point in which players spread their power over the entire spectrum, which results in a constant mutual interference. However, wireless channels are usually not fixed, and, in addition, are not estimated perfectly. This leads to payoff perturbations, which may cause the spectrally efficient equilibrium point to be unstable. This paper makes two contributions. First, we extend the Bayesian interference game, which was originally formulated and studied in the case of constant flat fading channels, for analyzing the case of frequency-selective block-fading or of time-varying block-fading channels. We show that the same strategy that improves the spectrum utilization in the game with fixed channels produces an efficient equilibrium point in the latter two cases as well. The second contribution is the incorporation of channel estimation errors into the game; i.e., we consider the case where each player has only a noisy estimate of its own channel gains. In this case, we show that the spectrally efficient equilibrium point is robust to small estimation errors. We demonstrate, via simulation, that the robustness and the improved spectral efficiency are maintained even if the channels are estimated via a training sequence as short as one.